Simplify the following expression: $ r = \dfrac{-5}{9} - \dfrac{2x + 9}{2x} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2x}{2x}$ $ \dfrac{-5}{9} \times \dfrac{2x}{2x} = \dfrac{-10x}{18x} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{2x + 9}{2x} \times \dfrac{9}{9} = \dfrac{18x + 81}{18x} $ Therefore $ r = \dfrac{-10x}{18x} - \dfrac{18x + 81}{18x} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{-10x - (18x + 81) }{18x} $ Distribute the negative sign: $r = \dfrac{-10x - 18x - 81}{18x}$ $r = \dfrac{-28x - 81}{18x}$